Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - Review Exercises: 32

Answer

$f'(t)=2t^4(5\cos{t}-t\sin{t}).$

Work Step by Step

Product Rule $f'(t)=((u(t)(v(t))’=u’(t)v(t)+u(t)v’(t))$ $u(t)=2t^5 ;u’(t)=10t^4 $ $v(t)=\cos{t} ;v’(t)=-\sin{t} $ $f'(t)=(10t^4)(\cos{t})+(-\sin{t})(2t^5)$ $2t^4(5\cos{t}-t\sin{t}).$
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